Vol. 6, No. 4, 2013

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Irreducible divisor simplicial complexes

Nicholas R. Baeth and John J. Hobson

Vol. 6 (2013), No. 4, 447–460

For an integral domain D, the irreducible divisor graph GD(x) of a nonunit x D gives a visual representation of the factorizations of x. Here we consider a higher-dimensional generalization of this notion, the irreducible divisor simplicial complex SD(x). We show how this new structure is a true generalization of GD(x), and show that it often carries more information about the element x and the domain D than its two-dimensional counterpart.

factorization, simplicial complex
Mathematical Subject Classification 2010
Primary: 13A05
Secondary: 55U10
Received: 6 August 2012
Revised: 12 October 2012
Accepted: 15 October 2012
Published: 8 October 2013

Communicated by Scott Chapman
Nicholas R. Baeth
Mathematics and Computer Science
University of Central Missouri
W. C. Morris 213
Warrensburg, MO 64093
United States
John J. Hobson
University of Central Missouri
Warrensburg, MO 64093
United States